Abstract: X-ray phase diffraction gratings can be designed to behave in a fashion similar to blazed gratings, directing the majority of the energy into certain desired orders. They should be easy to fabricate using conventional semiconductor production technology, and offer advantages in design flexibility and efficiency over conventional amplitude grating or blazed grating structures. As a multilayered structure, a phase grating has structure in depth as well as across the surface. Most theoretical analyses in the literature treat the embedded structure through simplifying approximations or assumptions. We will discuss a model which treats the embedded structure explicitly using the Fresnel-Kirchoff integral in the Fraunhofer diffraction limit. This approach produces a set of equations which are identical to the result for an amplitude diffraction grating except for an additional factor which depends on the phase relationships of the various surfaces in the multilayer stack.!12
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